Added failing test

tests/server/fastmcp/test_concurrency.py

@@ -0,0 +1,49 @@
+import anyio
+from pydantic import AnyUrl
+
+from mcp.server.fastmcp import FastMCP
+from mcp.shared.memory import (
+    create_connected_server_and_client_session as create_session,
+)
+
+_sleep_time_seconds = 0.01
+_resource_name = "slow://slow_resource"
+
+
+async def test_messages_are_executed_concurrently():
+    server = FastMCP("test")
+
+    @server.tool("sleep")
+    async def sleep_tool():
+        await anyio.sleep(_sleep_time_seconds)
+        return "done"
+
+    @server.resource(_resource_name)
+    async def slow_resource():
+        await anyio.sleep(_sleep_time_seconds)
+        return "slow"
+
+    async with create_session(server._mcp_server) as client_session:
+        start_time = anyio.current_time()
+        async with anyio.create_task_group() as tg:
+            for _ in range(10):
+                tg.start_soon(client_session.call_tool, "sleep")
+                tg.start_soon(client_session.read_resource, AnyUrl(_resource_name))
+
+        end_time = anyio.current_time()
+
+        duration = end_time - start_time
+        assert duration < 3 * _sleep_time_seconds
+        print(duration)
+
+
+def main():
+    anyio.run(test_messages_are_executed_concurrently)
+
+
+if __name__ == "__main__":
+    import logging
+
+    logging.basicConfig(level=logging.DEBUG)
+
+    main()